What stat effects the Sword Saint abilites?

I can't figure out if its physical or magical attacks, or perhaps both. I'm wondering rather to put attack boost or arcane strength to boost the damage to these attacks. I got Ramza as a Squire/dark knight, Orlandeau as a Sword Saint/mystic arts, Agrias as a hold knight/black magic, Beowulf as a spellblade/martial arts, and Meliadoul as a Divine Knight/white magiks. So all but Beowulf is using magic sword attacks and I really want to know when I stat level what job to level up as.

Thanks in advance!

It's a little complicated. Overall Ninja is generaly considered the best class to level up as. Ninja's have the best speed growth and some of the highest strength growth in the game.
These numbers are part of a formula that won't make sense unless you are really interested in mechanics, but you can use them to compare. The lower the number the better the stat growth.
P(Physical)-Attack:
Mime: 35
Meliadoul: 39
Knight: 40
Lancer: 40
Cloud: 42
Orlandu: 42
Ninja: 43
Samurai: 45
Monk: 48
Beowolf: 48
Agrias: 50
Speed:
Virtualy every class in the game has the same growth for speed (100), with the exception of Thieves(90) and Ninjas (80).
M(Magical)-Attack
Every every generic class in the game with the exception of Mime(35) has the same M-Attack growth (50). (Which is really stupid) The only specials that are exceptions are Cloud(46), Beowolf (45), Orlandu (42) & Ramza (48).

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Conclusions:For those who just want to be told what to do
Level up as a Ninja. It is the only class with good speed growth, has P-Attack growth almost equal to all the highest classes, and M-Attack growth doesn't really change depending on the class you level.


Fun Fact: Orlandu has higher M-Attack growth than any of the spell casters, but his P-Attack growth is overshadowed by both the Knight and Lancer.

EDIT: I spent so much time looking all this up I forgot about your first question.
All of the skills you mentioned are physical except for Beowolf's Magic Sword abilities. Both Attack Boost and Arcane Strength increase damage by 133% in most cases.
The bigger key for maximizing the success of Beowolf's abilities is his Faith stat. Magic spells are multiplied by the Faith stat as a percentage, so if you stick with the ~70FA he starts with the spell chances for success will all be multiplied by 0.7
WARNING: Do not raise any character's Faith above 94, they will leave your party perminantely and forever. No joke.

I have also done some research about stat growth and heard monks are the best, but if you are looking for speed ninjas win. I knew that Beowulf's special class was magic attack. Faith has a really big part in it. I just didn't know about the sword skills since they look magical but could be physical on some level.

Which would be better for a sword saint? Physical attack or magical attack?

All of the Sword Saint abilities are physical.
Monks are only good if you are looking to boost HP. IMO HP is one of the least useful stats in the game. By lv99 most enemies will do a ton of damage to you, or inflict some nasty status effects. The best way to go is to avoid taking damage at all by a combination of reaction abilities, staying out of range, and making sure to kill anything that comes in range before it has a chance to attack.

If you have a lv50 character with a 'raw' PA of 12 and a Speed of 9
Leveled as a Mime: PA 18.9 | Speed 11.9
Leveled as a Knight: PA 18.5 | Speed 11.9
Leveled as a Ninja: PA 18.4 | Speed 12.4
Leveled as a Monk: PA 18 | Speed 11.9

So the over all difference isn't massive.

Fun Fact: Priests have as much HP growth as knights.

Thanks for clarifying its physical attack. So Attack Boost is what I should add on to my team. I'm also in the middle of boosting back the bravery of one of my members. I sent one in to claim all the deep dungeon items and by the time I was done she was about to leave the party for good. Its nice to know that Ramza has a skill as a squire to raise bravery up to 97 in time. I'm really into poaching now. Trying to get all the items in the game.